integral from-θ to θ of 1/(θ^2)(θ-|x|)

פתרון

\int_{- θ}^{θ} \frac{1}{θ ^{2}} (θ - ∣ x ∣) d x

2 - \frac{∣ θ ∣}{θ}

צעדי פתרון

\int_{- θ}^{θ} \frac{1}{θ ^{2}} (θ - ∣ x ∣) d x

\int a \cdot f (x) d x = a \cdot \int f (x) d x

:הפעל את תכונת הליניאריות

= \frac{1}{θ ^{2}} \cdot \int_{- θ}^{θ} θ - ∣ x ∣ d x

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

:הפעל את תכונת הליניאריות

= \frac{1}{θ ^{2}} (\int_{- θ}^{θ} θ d x - \int_{- θ}^{θ} ∣ x ∣ d x)

\int_{- θ}^{θ} θ d x = 2 θ^{2}

\int_{- θ}^{θ} ∣ x ∣ d x = θ ∣ θ ∣

= \frac{1}{θ ^{2}} (2 θ^{2} - θ ∣ θ ∣)

\frac{1}{θ ^{2}} (2 θ^{2} - θ ∣ θ ∣)

פשט את:

2 - \frac{∣ θ ∣}{θ}

= 2 - \frac{∣ θ ∣}{θ}

\int_{0}^{1} x^{2} 30 x^{2} (1 - x)^{2} d x

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\int_{0}^{\frac{π}{2}} (sin (2 x))^{2} d x

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